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The test results are (95,92,90,90,83,83,74,60and 50) calculating the mean of the scores we
will use the formula 1/N(n1+n2+n3………..+ nk) where N is the total number of observation while
‘n’ is the value of each observation. Therefore substituting we get
1/9(95+92+90+90+83+74+60+50)=79.6667 . the mean is commonly referred to arithmetic mean or
sometimes referred to as expected value, it is the average performance of the score among the
students.
The median is the value that separates the higher half of the data. Given a set of data ,while
finding the median the first step is to arrange the values in either ascending or descending way. Using
the above set of data arranging the data (50,60,74,83,83,90,90,92,95) .the formula used to find the
middle number of a data set n is (n+1)/2 . therefore the middle number is (9+1)/2=5 hence the
median will be the fifth number which 83.
Mode is the most appearing value in a data set. It is the number with the highest frequency in
a data set. Considering the data above the most appearing values are 83 and 90 which have the
frequency of two. The mode values for our dataset are 83 and 90 .
Range is the difference between the maximum value and the minimum value in a data set.
Using the above dataset the maximum value is 95 and the minimum value is 50,therefore calculating
the range (95-50=45) hence the range is 45.
Variance can be calculated using the formula summation ((x-n)^2)/y-1.where x is the
observes value is the arithmetic mean and y is the number of observed variables. Therefore substituting
the values we get((50-79.667)^2+(60-79.667)^2+(74-79.667)^2………..(95-79.667)^2)/(9-1)=200.5
The standard variation is the square root of the variance therefore we find the square root
200.5 which is equivalent to 14.15
The best nethod of the discrete data is use of standard deviation and it is basically because it
standard deviation makes use of all data to calculate the spread of data from average while range
takes into considartion of only two numbers that is the minimum and the maximum. Standard
daviation measures the spread of data from mean . standard deviation gives weightage to deviation
of data by squaring it and for our case the standard deviation is high which means that it has a
greater weight . standard deviation is more precise since its not bias as compared to the others since
its not affected by extreme values which has an effect on mean. Therefore the use of standard
deviation is more effective and precise measure of central tendancy. Median takes into consideration
of only single value which makes it bias whereas mode cannot or may sometimes represent data
accurately and sometimes there maybe no mode in some data.
Calculation of one sample t test is executed using the formula t=(x-u)square root of n/s where
x= sample mean,u=population mean,n=number of observation,s=standard deviation. Replacing the
value we find (79.667-70)3/14.15=2.0495 . therefore the t calculated value is equivalent to 2.0495
hence the value is compared with the t value in the table. The use of t test is useful whan one is
trying to compare and tring to find if the sample mean and the population mean are equal, less or
more than the sample mean.
Reference
Statistics Solutions. (2013). One Sample T -Test [WWW Document]. Retrieved
from http://www.statisticssolutions.com/academic -solutions/resources/directory-ofstatistical-analyses/one-sample-t-test/.
Simon, Laura J.; "Descriptive statistics", Statistical Education Resource Kit, Pennsylvania State Department of
Statistics